What is the integral of 1/2-3cos^2(x) ?

The integral of 1/2-3cos^2(x) is -x-3/4 sin(2x)+C

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integral of 1/2-3cos^2(x)

integral

\frac{1}{2} - 3 cos^{2} (x)

- x - \frac{3}{4} sin (2 x) + C

Solution steps

\int \frac{1}{2} - 3 cos^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{2} d x - \int 3 cos^{2} (x) d x

\int \frac{1}{2} d x = \frac{1}{2} x

\int 3 cos^{2} (x) d x = \frac{3}{2} (x + \frac{1}{2} sin (2 x))

= \frac{1}{2} x - \frac{3}{2} (x + \frac{1}{2} sin (2 x))

Simplify

\frac{1}{2} x - \frac{3}{2} (x + \frac{1}{2} sin (2 x)) : - x - \frac{3}{4} sin (2 x)

= - x - \frac{3}{4} sin (2 x)

Add a constant to the solution

= - x - \frac{3}{4} sin (2 x) + C

\frac{1}{( x + x ^{2} )}

\frac{2}{t}

\frac{2}{1 - x ^{2}}

\frac{1}{( x + x ^{2} )}

\frac{ln ( x )}{( 1 + x ^{2} )}

What is the integral of 1/2-3cos^2(x) ?
The integral of 1/2-3cos^2(x) is -x-3/4 sin(2x)+C